Problem
Solve and graph: -3x + 7 > 16
📝Step-by-Step Solution
1
Isolate the variable term
Subtract 7 from both sides: -3x + 7 - 7 > 16 - 7
-3x > 9
2
Divide by the coefficient
Divide both sides by -3. IMPORTANT: When dividing by a negative number, FLIP the inequality sign!
-3x ÷ (-3) < 9 ÷ (-3)
3
Write the solution
x < -3
x < -3
4
Graph on a number line
Draw an open circle at -3 (because x is NOT equal to -3), then shade to the LEFT (because x is less than -3).
5
Check with a test value
Try x = -4: -3(-4) + 7 = 12 + 7 = 19 > 16 ✓. Try x = 0: -3(0) + 7 = 7 > 16 ✗. Correct!
✅Final Answer
x < -3
CRITICAL RULE: When multiplying or dividing both sides of an inequality by a negative number, you MUST flip the inequality sign (< becomes >, ≤ becomes ≥, etc.). This is the most common mistake in solving inequalities!
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